67,017 research outputs found
Error Correction in Quantum Communication
We show how procedures which can correct phase and amplitude errors can be
directly applied to correct errors due to quantum entanglement. We specify
general criteria for quantum error correction, introduce quantum versions of
the Hamming and the Gilbert-Varshamov bounds and comment on the practical
implementation of quantum codes.Comment: 9 pages, LaTex fil
On multicarrier signals where the PMEPR of a random codeword is asymptotically log n
Multicarrier signals exhibit a large peak-to-mean envelope power ratio (PMEPR). In this correspondence, without using a Gaussian assumption, we derive lower and upper probability bounds for the PMEPR distribution when the number of subcarriers n is large. Even though the worst case PMEPR is of the order of n, the main result is that the PMEPR of a random codeword C=(c/sub 1/,...,c/sub n/) is logn with probability approaching one asymptotically, for the following three general cases: i) c/sub i/'s are independent and identically distributed (i.i.d.) chosen from a complex quadrature amplitude modulation (QAM) constellation in which the real and imaginary part of c/sub i/ each has i.i.d. and even distribution (not necessarily uniform), ii) c/sub i/'s are i.i.d. chosen from a phase-shift keying (PSK) constellation where the distribution over the constellation points is invariant under /spl pi//2 rotation, and iii) C is chosen uniformly from a complex sphere of dimension n. Based on this result, it is proved that asymptotically, the Varshamov-Gilbert (VG) bound remains the same for codes with PMEPR of less than logn chosen from QAM/PSK constellations
Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes
Given positive integers and , let denote the maximum size
of a binary code of length and minimum distance . The well-known
Gilbert-Varshamov bound asserts that , where
is the volume of a Hamming sphere of
radius . We show that, in fact, there exists a positive constant such
that whenever . The result follows by recasting the Gilbert- Varshamov bound into a
graph-theoretic framework and using the fact that the corresponding graph is
locally sparse. Generalizations and extensions of this result are briefly
discussed.Comment: 10 pages, 3 figures; to appear in the IEEE Transactions on
Information Theory, submitted August 12, 2003, revised March 28, 200
On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime
As the mobile application landscape expands, wireless networks are tasked
with supporting different connection profiles, including real-time traffic and
delay-sensitive communications. Among many ensuing engineering challenges is
the need to better understand the fundamental limits of forward error
correction in non-asymptotic regimes. This article characterizes the
performance of random block codes over finite-state channels and evaluates
their queueing performance under maximum-likelihood decoding. In particular,
classical results from information theory are revisited in the context of
channels with rare transitions, and bounds on the probabilities of decoding
failure are derived for random codes. This creates an analysis framework where
channel dependencies within and across codewords are preserved. Such results
are subsequently integrated into a queueing problem formulation. For instance,
it is shown that, for random coding on the Gilbert-Elliott channel, the
performance analysis based on upper bounds on error probability provides very
good estimates of system performance and optimum code parameters. Overall, this
study offers new insights about the impact of channel correlation on the
performance of delay-aware, point-to-point communication links. It also
provides novel guidelines on how to select code rates and block lengths for
real-time traffic over wireless communication infrastructures
Nonparametric Bounds and Sensitivity Analysis of Treatment Effects
This paper considers conducting inference about the effect of a treatment (or
exposure) on an outcome of interest. In the ideal setting where treatment is
assigned randomly, under certain assumptions the treatment effect is
identifiable from the observable data and inference is straightforward.
However, in other settings such as observational studies or randomized trials
with noncompliance, the treatment effect is no longer identifiable without
relying on untestable assumptions. Nonetheless, the observable data often do
provide some information about the effect of treatment, that is, the parameter
of interest is partially identifiable. Two approaches are often employed in
this setting: (i) bounds are derived for the treatment effect under minimal
assumptions, or (ii) additional untestable assumptions are invoked that render
the treatment effect identifiable and then sensitivity analysis is conducted to
assess how inference about the treatment effect changes as the untestable
assumptions are varied. Approaches (i) and (ii) are considered in various
settings, including assessing principal strata effects, direct and indirect
effects and effects of time-varying exposures. Methods for drawing formal
inference about partially identified parameters are also discussed.Comment: Published in at http://dx.doi.org/10.1214/14-STS499 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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